Question

Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

• A. 40008
• B. 20008
• C. 20808
• D. 10808

Answer 1

The Correct Option is C

Anil invested \(22000\) for \(6\) years at \(4\%\) interest compounded half-yearly.

Amount = \(22000(1+\frac {2}{100})^{12}\)

\(= 22000 (1.02)^{12}\)
Suppose, Sunil invest \(P\) rupees for \(5\) years at \(4\%\) C.I. half-yearly and \(10\%\) S.I. for \(1\) additional year.

Amount = \(P(1+\frac {2}{100})^{10} \times 1.1\)

\(= P (1.02)^{10} \times 1.1\)
Given, both amounts are same,

\(22000 (1.02)^{12}= P (1.02)^{10} \times 1.1\)
\(P = \frac {22000 (1.02)^{12}}{(1.02)^{10} \times 1.1}\)

\(⇒P = \frac {22000 (1.02)^{2}}{1.1}\)
\(⇒P=20808\)

So, the correct option is (C): \(20808\)